Ben is 3 times as old as Luis. Four years ago, Ben was 5 times as old as Luis. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Ben and Luis. Let Ben's current age be $b$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $b = 3l$ Four years ago, Ben was $b - 4$ years old, and Luis was $l - 4$ years old. The information in the second sentence can be expressed in the following equation: $b - 4 = 5(l - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = b / 3$ . Substituting this into our second equation, we get: $b - 4 = 5($ $(b / 3)$ $- 4)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 4 = \dfrac{5}{3} b - 20$ Solving for $b$ , we get: $\dfrac{2}{3} b = 16$ $b = \dfrac{3}{2} \cdot 16 = 24$.